After responding to a post on this topic and getting positive feedback from many people, I decided to write an FAQ on it. Since the FAQ forum is currently closed for a bit, I decided to post it here. It's pretty basic stuff, but if you want anything added or changed, just post here. Without further, delay, here it is...
I'm sure by now, the vast majority of you have at least a couple fans in your system. You may have also noticed that a fan's operating noise is measured on the decibel (dB) scale. Bels and, more specifically decibels are a logarithmic measurement scale use to quantify relative levels of energy (be that acoustic energy, electrical, etc.). Filip has posted a simplified explanation on decibels
here, so I won't go into much detail. I will, however, go into detail about the applications of decibels and using them to determine your overall system noise.
Right from the start, it's necessary to understand that decibels, as mentioned before, are a logarithmic scale. In other works, 20 dB is not twice as loud as 10 dB, and 5 dB + 5 dB is NOT 10dB. I'll outline the basic method for determining decibels and their conversions to and from "true" energy, so that you can calculate exactly how loud a computer setup may be.
First we need to acknowledge that for a given quantity of x, you can find the decibel measurement y as follows:
y = 20 log (x)
Note: All log functions are base 10.
In this case, the "true" energy is given as x and could be in volts or any other measurement of energy. What matters is that x is measured on a linear scale, and y is measured on a logarithmic scale. As many people are familiar with, when you work with linear scaled measurements, all the nice basic arithmetic rules apply (ie. 5+5=10). If you're still not following why this is useful, let’s work backwards.
In the case of computer noise, all the components noise levels are given in dB. Since the dB scale is logarithmic, we can’t simply just add the noise levels together. Heck, with 4 fans operating at 35 dB, straight addition would yield 140 dB (the noise level of a jet engine at 100’). Now I know some hardcore water/phase enthusiasts may disagree, but a fan cooled PC certainly doesn’t come close to a jet engine in terms of noise. This is where the linear scale comes into play.
Given a fan’s noise level is say 30 dB. Say you want 3 of those fans. By now you should know that the result will NOT be 90 dB. Instead, we’ll take these steps.
- Convert all dB measurements to a linear scale
- Add up all the linear measurements of all your components
- Convert the final sum back into a dB measurement
In this case, for a 30 dB fan, we get:
30 = 20 log (x)
x = 10^ (30/20)
x = ~31.623
So each fan will have a linear energy measurement of ~31.623. Since we’re using 3 fans
Total energy = 3 * 31.623
= 94.868
Now, we know the total system will have an approximate energy of 94.868. To figure out how loud the system will be in dB, we use the original conversion.
y = 20 log (94.868)
y = 39.542 dB
As shown above, using 3 30dB fans does NOT mean your computer will be 90dB. However, since the scale is logarithmic, you should note this table of values:
Perceptions of Increases in Decibel Level
Imperceptible Change - 1dB
Barely Perceptible Change - 3dB
Clearly Noticeable Change - 5dB
About Twice as Loud - 10dB
About Four Times as Loud - 20dB
Table source: http://www.gcaudio.com/resources/howtos/loudness.html
Using this table, and all of our knowledge of the decibel scale, we can safely say that using three 30 dB fans will be about twice as loud as a single 30 dB fan (since it’s about 9.5 dB louder than a single fan).
Quick Summary:
1. For each component, calculate the linear energy, x, using
x = 10^(y/20), where y is the given noise level in dB
2. Add up all your x values to get the total energy
3. Convert your total energy back to decibels using:
Y = 20 log (X), where X is the sum of all the x’s calculated for each component.
Hopefully you guys were able to follow this, and you’ll be able to put it to use when working on a cooling project and trying to figure out how loud that computer really will be. I realize that I used the term energy fairly loosely throughout this guide, but it wasn't my intention to make scientists and engineers out of you. This is just a simple reference to help some people who aren't quite sure of the math behind decibels.